There’s a book series based on using cloning and memory storage to accomplish very similar things called Undying Mercenaries. The main difference is instead of copying someone and keeping the copy on ice they have cybernetic implants that send engrams of their mind to remote storage, and if they die a clone can be rapidly grown and those stored memories saved to it. It gets pretty schlocky as time goes on, but it’s a fun premise to play around with.
There is a chapter or two from a book by philosopher Derek Parfit that tackles the transporter issue pretty head-on. It draws what I feel to be a pretty compelling distinction between the continuity of your conscious mind, referred to as Relation R, and the personal identity that is lost when using the transporter. He then asks which is more important. Worth a read if this stuff interests you.